# Almost fixed-point-free automorphisms of prime order

Open Mathematics (2011)

- Volume: 9, Issue: 3, page 616-626
- ISSN: 2391-5455

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topBertram Wehrfritz. "Almost fixed-point-free automorphisms of prime order." Open Mathematics 9.3 (2011): 616-626. <http://eudml.org/doc/269477>.

@article{BertramWehrfritz2011,

abstract = {Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the case p = 2 is discussed.},

author = {Bertram Wehrfritz},

journal = {Open Mathematics},

keywords = {Soluble group; Groups of finite Hirsch number; Groups of finite rank; Fixed points of automorphisms of prime order; soluble groups; groups of finite Hirsch number; groups of finite rank; automorphisms of prime order; fixed-point-free automorphisms; characteristic subgroups of finite index},

language = {eng},

number = {3},

pages = {616-626},

title = {Almost fixed-point-free automorphisms of prime order},

url = {http://eudml.org/doc/269477},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Bertram Wehrfritz

TI - Almost fixed-point-free automorphisms of prime order

JO - Open Mathematics

PY - 2011

VL - 9

IS - 3

SP - 616

EP - 626

AB - Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the case p = 2 is discussed.

LA - eng

KW - Soluble group; Groups of finite Hirsch number; Groups of finite rank; Fixed points of automorphisms of prime order; soluble groups; groups of finite Hirsch number; groups of finite rank; automorphisms of prime order; fixed-point-free automorphisms; characteristic subgroups of finite index

UR - http://eudml.org/doc/269477

ER -

## References

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- [14] Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)

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